EVOLUTION OF ROLL PATTERNS IN RAYLEIGH-BENARD CONVECTION IN A RECTANGULAR LAYER - A NUMERICAL STUDY

摘要

A three-dimensional unsteady numerical simulation was carried out to unravel the buoyancy-induced flow in a bottom-heated shallow rectangular box with perfect conducting side walls. The Navier-Stokes and energy equations were discretized by the higher order finite difference approximations and solved by the explicit projection method. Computations were specifically carried out for water (Pr = 3.5) and air (Pr = 0.71) in a box of aspect ratios 10.6 X 5.3. The results for the water layer indicated that in raising the Rayleigh number (Ra) suddenly from zero to a value slightly above that for onset of convection, square cells were induced that later gradually merge to form parallel rods along the short sides. Soft patterns were induced where Pa was abruptly raised from 0 to 4 Ra-cr. The augmentation of wavelength in a parallel roll system was found to result from the disappearance of the rolls near the short sides and the expansion of the other rolls. In an air layer the increase in the roll size resulted from the skew-varicose instability and the combination of the adjacent rods. [References: 18]